
Class 

Book 

Copyright^ . 



COPYRIGHT DEPOSIT. 



DISTRIBUTION OF OPPORTUNITY FOR 
PARTICIPATION AMONG THE VARIOUS 
PUPILS IN CLASS-ROOM RECITATIONS 



BY 

ERNEST HORN, PH.D. 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION, No. 67 



PUBLISHED BY 

Qfearijrra (Eollegp, (Eulumbta Snttttrattg 

NEW YORK CITY 

1914 



Ponograph 



\3^ 



Copyright, 1915, by Ernest Horn 



" 



1 
•opyjtieiX 



-7 1915 

©CLA410134 



TABLE OF CONTENTS 

PAGE 

I. Purpose of the Investigation 1 

II. How the Data were Secured 3 

III. Reliability of the Data 10 

IV. Organization of the Data 12 

V. The Distribution of Participation by Grades. . 15 

VI. The Relationship Between General All-Round - 

Ability and Amount of Participation....... 19 

VII. Relationship Between Ability in Special Sub- 
jects and the Amount of Participation in 

Those Subjects 27 

VIII. Educational Implications 35 

Appendix 38 



in 



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in 2011 with funding from 
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INDEX TO TABLES 

PAGES 

I. The Distribution of Opportunity for Participation, for 

Individual Teachers, by Grades 14 

II. Medians Found from Table 1 16 

III. The Effect of a Small Number of Records 17 

IV. Variability of the Percentages in Table 1 17 

V. The Relationship Between General Ability and Amount 

of Participation, for Individual Teachers, by Grades. 21-22 

VI. Medians for Table V 23 

VII. 75 and 25 Percentiles for Table V 24 

VIII. Variability for Table V 25 

IX. Relationship Between Ability in Special Subjects and 
the Amount of Reciting in Them, for Individual Teach- 
ers, by Grades 28-31 

X. Medians for Table IX by Subjects 32 

XI. Variability for Table IX by Subjects 33 



THE DISTRIBUTION OF OPPORTUNITY FOR PARTI- 
CIPATION AMONG THE VARIOUS PUPILS IN 
CLASS-ROOM RECITATIONS 



PURPOSE OF THE INVESTIGATION 

The final test for any educational procedure whether it be 
making, administrating, or teaching the course of study, is its 
effect on individual pupils in the school. The studies on school 
grading, size of classes, questioning, and other phases of class 
management show that the problem of reaching the individual 
child has been long before the teaching profession. Recently the 
demand for classes for unusual children, whether subnormal or 
supernormal, has given additional emphasis to its importance. 
In discussing the question with classes in principles of education 
and in working over the problems outlined above, the author 
has felt many times the need of definite knowledge, with regard 
to the exact nature of the practice in meeting this difficulty of 
reaching the individual child. To supply some of these data is 
the purpose of this investigation. 

To state more definitely, the purpose of this investigation is 
to ' discover the distribution of opportunity for participation 
among the various pupils in class-room recitations. By partici- 
pation is meant any response on the part of the pupil, whether 
in word or in action. It is used alternately with reciting and 
pupil recitation and as synonymous with them. The investi- 
gation was planned to secure data which could be organized 
about the following sub-problems : (1) How equally is the oppor- 
tunity for participation distributed ? (2) What is the relation 
between the amount of reciting done and the general all-around 
ability of the pupil ? (3) What is the relation between the 
amount of reciting done in each subject and the special ability 
in this subject ? (4) How many opportunities for participation 
for class work does the pupil have per hour ? (5) What propor- 

1 



2 Participation Among Pupils in Class- Room Recitations 

tion of the pupil's recitations are utter failures ? (6) What is 
the relative amount of time given to talking as a form of 
participation as compared with other activities ? (7) How- 
many of the pupil's recitations consist of consecutive participa- 
tions without the recitations of any other pupils intervening ? 
(8) What is the length of pupil's recitations ? 

As will be seen in the treatment which follows, not all of this 
material has been utilized in this study. 



II 

HOW THE DATA WERE SECURED 

The data which are incorporated in this study, and from which 
the generalizations of the treatment are drawn, were collected 
by the author and by principals, superintendents and super- 
visors in the field. 

Records for one school (Speyer School, Teachers College, 
Columbia University) were made personally by the author. 
This school was used throughout the investigation as a source of 
suggestion, and as a control of methods of making records. 
Records were marked for three weeks before the directions which 
were to be sent to those who were to cooperate, were put in 
final form. The collecting of data then continued until, through 
a mistake of an assistant, some of the teachers were made aware 
of the nature and purpose of the investigation. This, unfor- 
tunately, closed the rooms of these teachers as sources of data 
to be used in this study. 

Requests for cooperation were not sent out broadcast to prin- 
cipals, superintendents, and supervisors in the field, but to a 
selected group who are known to the author, personally or by 
recommendation, to be interested and competent in making 
statistical investigations. To each individual so selected, the 
following set of directions was sent, along with a letter which 
explained the purpose of the study: 

SHEET 1. GENERAL DIRECTIONS 

1. Teachers should know nothing of the data being collected nor their 

purpose. 

a. Should any teacher give evidence of understanding what is 

being done, this fact should be reported. 

b. If you have been putting special emphasis upon the equal 

distribution of opportunity for recitation amongst the various 
pupils in the class, this fact should be reported. 

2. The seating plan method of marking recitation records is preferable, 

both because of the greater accuracy and because of the greater ease 
with which the record can be made. 

3. Please send in all data collected. In case any record seems incomplete 

or inaccurate, mark it incomplete or inaccurate, but send it in. 

3 



4 Participation Among Pupils in Class-Room Recitations 

4. As you will see upon examining the record sheets, Sheet 2 contains the 

actual directions for making records and should be thoroughly under- 
stood. 

5. Two copies of Sheet 3 and of Sheet 4 are sent. Both should be marked 

at the same time, one being retained by you and the other returned 
to me. 

6. I have attempted to put into these directions everything which could 

influence the usefulness of the data being collected. If, in your judg- 
ment, any element has been neglected, or if a re-statement of any part 

seems desirable, will you kindly notify me of the same at your earliest 

convenience ? 

SHEET 2. PROCEDURE WITHIN CLASS ROOM 
I. Only one record should be taken on one sheet of paper. 
II. Write at the top of the page as follows : 

Grade Class Time Date Teacher 

(1) (Geography) (10-10:30) (Oct. 6th) (Kinne) 

III. Mark the name of each pupil absent during the recitation so: 

John S. 

(abs.) 
IV. (1) a. For each recitation or request for recitation, mark O (under the 
name, in case the seating plan is used ; after the name, in case 
the name list is used. See samples 1 and 2.) 

b. In case the pupil responds by doing something, mark □. For 

example, in the case of the square marked under the name of 
Grace M., in Sample 1, this mark was made when Grace beat 
the white of an egg. The same mark (□) is used for diagrams 
drawn on the board, etc. 

c. When the pupil recites more than once without the recitation of 

any other pupil intervening, interlink the circles so: GD. 
Thus GX2D denotes four recitations without the recitation 
of any other pupil intervening, 
d. In case the pupil fails utterly, mark " F " inside the circle or square 
so: ® \f\. This may be omitted if found too difficult to make. 
(2) When the whole class says or does something as a class, a circle or 
square may be drawn after the name of the grade. See at 
the top of the page in samples 1 and 2. This may be omitted 
if found too difficult to make. 
V. If conditions are present which may influence the interpretation of the 
records made as described above, such a fact may be noted in writing 
on the back of the sheet on which the record was made. 
VI. If the marks asked for under IV, (1), c, d; or IV, (2) are omitted, this 
fact should be noted and reported. 



OOnOO 
Grade 1 
Frank H. 
OO 


Reading 
Anna M. 

ooo 


SAMPLE 

10—10:30 
John R. 
OO 


1 

October 6th 
Ferdinand C. 


Small 

Lucy W. 
® OO 


Marie R. 
OO 


Grace M. 
On 


Stewart S. 
O 


Joseph N. 


Marion R. 


Robert V. 


Harold N. 
Abs. 


Egbert I. 
O 


William A. 
OO 


Hortense D. 
OO 


Eugene C. 
OO 


Florence E. 

OGD 


Jacques P. 
OO 


Gobin H. 
OOO 


Margaret M 
OnOO 



How the Data Were Secured 





SAMPLE 2 




OOdOO 






Grade L Reading 


10—10:30 


October 6th 


Anna B. 






Egbert I. 

Eugene C. 

Ferdinand G. 






Frank B. 






Florence E. QD 






Gobin H. 






Grace M. □ 






Abs. 






Hortense D. 






Jacques P. 
John R. 
Joseph N. 
Lucy W. ® 
Margaret M. □ 
Marie R. GD 






Marion R. 






Robert V. 






Stewart S. 






William A. 







Small 



As you can see, this method can be used satisfactorily only when 

(a) A teacher calls the pupil by name each time, 

(b) Or when the individual making the record is himself acquainted with 

all the pupils in the class. 

SHEET 3. REPORT OF RECORD BEING MADE 

In order that I may have information to aid me in the search for data, 
will you kindly underline the kinds of records which you will undertake to 
make ? If possible, without too great inconvenience to you, I should like 
to have a record for each grade under your supervision, as described in 
1 a-b-c-d, and 2. (See below.) If you cannot take time for this, data gathered 
as described in 3 will be very acceptable. (By each grade is meant one first 
grade, one second, etc.) 

1 . Records of a grade for one day. This may be made up : 

a. Of one whole day's observing. (Say Wednesday.) Please underline 

the grades for which you can make such records. 
Grade I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. 

b. Of two half days. (Say Wednesday morning and Thursday after- 

noon). Please underline the grades for which you can make 
such records. 
Grade I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. 

c. Of four quarter days in case there is a mid-morning and mid-after- 

noon recess. Please underline the grades for which you will make 
such records. 
Grade I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. 

d. Of each subject on the program, the records being taken over a 

period of several days. (This period should not be more than three 
weeks.) 

Note: (1) a, b and c are much more economical, as well as more satisfactory, 
since visits are more easily fitted to the program and with less 
waste due to changing from class to class. 
(2) If the teacher in whose class a record is being taken is made ner- 
vous by long visits, c or d should be used instead of a and b. 



6 Participation Among Pupils in Class- Room Recitations 

(3) In case one or all of these records are made, please fasten the 
records with a clip and mark them (1-a, 1-b, etc., as the case 
may be). 

2. Records of one subject in one grade for three or more successive days. 

For example, History, Grade VI, Speyer School, Monday, Tuesday, 
Wednesday, Thursday. 

3. Records taken during the ordinary course of supervision. I should like 

to have at least three and if possible ten of those records for each grade . 

SHEET 4. RANK OF THE PUPILS IN THE CLASSES FOR WHICH 
RECORDS ARE TAKEN 
Please underline below the basis in your system upon which such ranking 
can be made. 

1. The grades of the pupils for last year and for the months completed so 

far this year. Are these grades given in 

a. Numbers ? 

b. Letters ? 

2. Ranking of the pupils by the teacher in order of their abilities. Below 

is a sample of such ranking. 

Grade VI. School X. 

a. Will L., Mildred L. 

b. Edith W., Dorothy N., Wilma S., James K., Elizabeth B. 

c. John S., Minnie S., Robert P., Dan D., Fred. P., Harry F. 

d. Ruth R., Frank D. ( Nellie T., Wesley E. 

e. Perry E. 

f. Esther S. 

Note 1: a, b, c, etc., denote a difference of considerable amount; other- 
wise the ranking is merely in order of ability. For example, Will L., 
Mildred L., and Edith W., are the three pupils ranking highest in 
ability. 

Note 2 : It must be kept in mind that this ranking is according to ability 
and not according to accomplishment. It is meant to give the teacher's 
judgment of what the child can do, rather than to furnish a record of 
what he has already done. 

3. Has any test of general intelligence (such as the Binet tests) been given ? 

If so, are the results available for use in the ranking of pupils in the 
classes reported upon ? 

Two copies of Sheet 3 and Sheet 4 were sent, one being marked 
" Please keep this Sheet," and the other, " Please return this 
Sheet at your earliest convenience." 

As the duplicates of Sheets 3 and 4 began to come in, it became 
evident that a new Sheet 4 would have to be sent out, for the 
following reasons : 

1. The variation in modes of grading was very great. 

2. In many cases only four marks were used — 1, 2, 3, 4, or 

a, b, c, d. 

3. Even these grades could be sent only with great inconven- 

ience to those cooperating. 

4. The grades were not of a nature which would make possible the 

separation of the pupils into quartiles according to ability. 



How the Data Were Secured 7 

Since this division was necessary to the treatment to be fol- 
lowed in the study, a new Sheet 4 was sent out to guide in making 
the ranking desired. Below follows a copy of this sheet: 

SHEET 4. RANK OF THE PUPILS IN THE CLASSES FOR WHICH 
RECORDS ARE TAKEN 

I. The rankings of the pupils in ability, as described in II, A and B of this 

sheet, should be returned with the records. Each ranking should be 
plainly marked, as for example: School X, Grade 1, Ability in Reading, 
Miss Small; or School X, Grade 1, General Ability, Miss Small. 

II. Ranking of the pupils by the teacher in order of their abilities. (This is 

very desirable.) 

A. The rank of pupils in each grade in each subject for which records of 

recitations have been made, according to the following plans: 

1 . The rankings should be by the teacher who taught the class 

when the record was made. 

2. Pupils should be ranked in order of ability. It must be kept 

in mind that this ranking is according to ability and not 
according to accomplishment. It is meant to give the 
teacher's judgment of what the child can do rather than to 
furnish a record of what he has already done. 

3. In case the teacher cannot decide which of two pupils is the 

better, one should be placed arbitrarily above the other. A 
question mark should then be placed after each pupil whose 
position in the list is in doubt. This same arbitrary placing 
should be used in case more than two pupils seem to be 
equal in ability. 

4. In case differences of considerable amounts appear between 

groups within the same class, this grouping can be indicated 
as in the sample below: 

History — 8th Grade, Room 31 — School X 

a. Pearl, L. 

b. John C, Lloyd M. 

c. Mary T., Ruth, Carrie P. 

d. Frances, L., John B., Anna K. 

e. Sarah H., Charles T. 

f. Paul A., Bess T., Susie S., Helen. 

g. Minnie, Sam P. 
h. Roy O., Mary W. 

a, b, c, etc., denote differences of considerable amount. 
Otherwise, the ranking is in order of -ability. For example, 
in this list, Pearl L., John C, Lloyd M., Mary T., and Ruth 
are the five best students ranking in the order given. 
Between groups a, b, c, etc., however, there is, in the opinion 
of the teacher, a greater difference than between the individ- 
uals within any of the groups. 

B. The general ability of the class, ranked after the method described 

in II A. 
This ranking is meant to be an answer to the question : How do the 
pupils of this grade rank in general all-round ability? This ranking, 
as in A- 1, 2, 3, 4, is to be made according to what, in the teacher's 
opinion, the pupil has in the way of native ability. Below is the rank- 
ing in general ability of the same class which was ranked in History 
under II A. 



8 Participation Among Pupils in Class- Room Recitations 

General Ability — 8th Grade — School X 

a. Mary T., Pearl L., Lloyd M., Ruth. 

b. Anna K., Carrie P., John C. 

c. Paul A., Charles T. 

d. John B., Sarah H., Frances L., Bess T. 

e. Roy O., Susie S., Helen, Mary W. 

f. Minnie, Sam P. 

Obviously, Mary T., Pearl L., Lloyd M., Ruth, and Anna K. are, 
in the opinion of the teacher, the five best pupils. The difference 
between Ruth and Anna K. is greater than the difference betweeen 
Ruth and Lloyd M. 

Records were made according to these directions in the 
following schools : 

Bridgeport, Conn. 

Training School, Colorado State Teachers College, Greeley, Colorado. 

Denver, Colorado. 

Boise, Idaho. 

Decatur, Illinois. 

Middleton, Indiana. 

Bremen, Indiana. 

Hancock, Michigan. 

Training School, Kalamazoo State Normal School, Michigan. 

Teachers College, Elementary School, School of Education, University 

of Missouri, Columbia, Missouri. 
Mexico, Missouri. 
Millville, New Jersey. 
Paterson, New Jersey. 
New York City, Public School 64. 
New York City, Public School 86. 
Teachers College, Columbia University, Horace Mann Elementary School, 

and Speyer School. 
Chattanooga, Tennessee. 
El Paso, Texas. 
Princeton, Missouri. 
Oswego State Normal School, New York. 



For obvious reasons, the schools which sent in records are not 
identified in the discussion which follows, but are referred to by- 
Roman numerals. The teachers are referred to by Arabic 
numerals. Below follows the teachers' numbers which corres- 
pond to the various schools. A complete key to the schools 
and to the teachers is on file in the library at Teachers College, 
Columbia University. 



How the Data Were Secured 
School Teachers School Teachers 



I 


1- 10 


XII 


128-159 


II 


11- 32 


XIII 


160-175 


III 


33- 37 


XIV 


176-186 


IV 


38- 56 


XV 


187-190 


V 


57- 63 


XVI 


191-194 


VI 


64- 84 


XVII 


195-198 


VII 


85-100 


XVIII 


199-203 


VIII 


101-110 


XIX 


204-209 


IX 


111-117 


XX 


210-212 


X 


118-123 


XXI 


213-229 


XI 


124-127 







The author was at first disposed to include in the directions 
given on Sheet 2, three other requests: (1) That all pupils who 
volunteer, be marked so (V). (2) That the value of the con- 
tribution of each pupil recitation be indicated on a scale of one, 
two, three, four and five. (3) That each question asked by 
the pupil be indicated so (Q) . These requests were not included 
because it was feared that the burden of doing so much might 
cause supervisors in the field to refuse to cooperate at all and 
because of the great difficulty of keeping all of these items in 
the mind of the recorder in such a manner as to insure that all 
the data be accurately taken. These problems, with many others 
which have been suggested during the progress of the investi- 
gation, have been left for future study. 

All but six schools, namely, VIII, X, XV, XVI, XVII, 
XIX, and XXI, used the seating plan method of making the 
records. This fact adds to the reliability of the record because 
of the check afforded by having both the name of the pupil 
called upon and his position in the room, to guide the recorder. 

All persons marked all data asked for on Sheet 2. The remarks 
asked for under V, Sheet 2, were highly satisfactory in affording 
a basis upon which to accept or reject records, and for the proper 
interpretation of records accepted. Some of the records con- 
tained additional information which will be referred to in the 
general discussion which is to follow. 



Ill 

RELIABILITY OF THE DATA 

The first set of directions for collecting the data treated in 
this thesis was mailed October 21, 1913. The first record 
made by those who cooperated was made November 10, 
1913. Most of the records were made during January, 1914. 
Even at the time when the first records were made, the 
teachers' habits of procedure must have been fairly well 
established and a reasonable opportunity given them to know 
the rank of the pupils, at least well enough to place them in the 
four quartile groups which have been used in making comparisons 
in this - study. Records were received and embodied in this 
study which came in as late as March 14. As far as a particular 
time in the progress of the school year can influence the methods 
of teaching, these records should be representative of ordinary 
school work. 

Records were made in the classes of 229 teachers in twenty- 
two different schools, in nineteen different systems, in eleven 
different states. As may be seen from the list of schools given 
in Part II, these schools represent a wide geographical distribu- 
tion. Records were taken from the kindergarten, from each of 
the elementary grades, from the high school and from the college. 
Only a few, however, were taken for the kindergarten and for 
the college. The only principles of selection were the effort to 
secure a wide distribution of type and the effort to secure com- 
petent cooperation. It seems very unlikely that these efforts 
affected any selection among school systems which would render 
the data unreliable as adequately describing general school 
practice in large and small cities throughout the country. 

All data received were used, which were clear, which were free 
from unusual circumstances indicated on the record (according 
to the request made upon Sheet 2 of the directions) , and which 
were in the hands of the author in time to be embodied in this 
study. This precludes the possibility of selection by the author. 

10 



Reliability of the Data 11 

The material, moreover, is left as far as possible in its original 
form and is given separately for each grade and subject. All 
data not rejected for the reasons just stated, are given in the 
various tables, even though in some cases the number of records 
is too small to constitute conclusive evidence. These are given 
as the only data available to the author at this time, and to 
allow any, who care to do so, to fill out the very apparent gaps. 
The generalizations found in the last chapter are made from 
data which are ample enough to be practically conclusive. A 
very little thought would show how stupendous a task it would 
be to include in a single study sufficient data for an ample treat- 
ment of each of the headings under which the data have been 
grouped. 

The likelihood of error on the part of recorders seems very 
small, considering the manner in which such a possibility was 
guarded against in the directions on Sheet 2. The only mistakes 
which may have crept in are those of omitting the mark for a 
pupil recitation or of placing a mark under the name of the wrong 
pupil. Even if the possibility of such omissions or mistakes be 
admitted, it is very unlikely that such omissions or mistakes 
should affect one quartile more than another. 

All that is desired in this study is to show how the teacher 
distributed the opportunity for recitation among the various 
pupils according to their ability as she believes this ability to be. 
It is to measure the effect of her conscious method in so far as 
she has one, with regard to this distribution. Even if it be desired 
to know how this opportunity is distributed, according to the 
actual ability of the pupils, there are no tests at present more 
reliable than is the teacher's judgment, for the purpose of 
affording a basis upon which to rank the pupils in general all- 
round ability or in ability in special subjects. . 



IV 

ORGANIZATION OF THE DATA 

The first step in the organization of the data consisted in the 
transfer of the data from the record sheets to the ranking sheets, 
the number of recitations of each pupil in each subject being 
placed opposite his name in the ranking list. The following 
procedure was observed : 

1. In case any ranking or record was obscure, it was laid aside 

until further information could be obtained. In case it 
contained obscurities which could not be cleared up by 
additional information, it was thrown out. Following 
under 2, is the only exception to this rule: 

2. When the position of any pupil in the ranking sheet or his 

marking on the record sheet was obscure, his name and 
record were thrown out. In case the record showed many 
such obscurities, the whole record was thrown out. 

3. Treatment of absentees : In case a single record was available 

for a given class, absentees were counted as not belonging 
to the class. The same rule was followed in cases where a 
pupil was absent in all recitations for which records were 
made. In case a pupil was marked as present at some of 
the recitations, but absent at others, he was given the aver- 
age of his other recitations as his record for the days on 
which he was absent. In adding all recitations to find the 
total amount done by him, if the sum involved a fraction, 
an additional unit was given in cases which amounted to 
five-tenths (.5) or more. When the fraction amounted to 
less than five-tenths, it counted as zero. This method is 
somewhat crude, but is as likely to affect one part of the 
ranking list as another, and so has, practically, no influence 
on any of the quartile summaries as reached. 

4. Quartile groupings for comparisons : The quartile was selected 

because it represents the mode of grouping which is probably 
the most conventional. Some summaries were arranged 
12 



Organization of the Data 13 

also as textiles and quintiles but seemed to add nothing to 
the information given by the quartile grouping. Grouping 
according to the normal curve of distribution also suggested 
itself, but the great increase in the labor of computation 
seemed to offer little additional return as a reward. 

The conventional method of finding the quartile divisions 
was used, these divisions being taken as representing the 
first, second, third and fourth quarters of the class, counting 
from the end of the ranking list which represented the great- 
est amount of ability. When the quartile division point 
fell within a measure, the fractional part was taken. On 
account of the greater accuracy of this method, this pro- 
cedure was felt to be valuable enough to offset the possible 
objection that this procedure necessitated splitting the 
recitation measures of one student. For example, with 
twenty-six pupils, with recitation records running 13, 9, 8, 
10, 7, 2, 4, etc., the first quartile division falls within 4, the 
recitation records of the seventh pupil, making the sum of 
the pupil recitations of the first quartile, 51. When this 
sum was a complex fraction, the exact fraction was used in 
determining the percentages which are given in the various 
tables. The same method of finding quartile division 
points and percentages was used for comparisons by rank 
in special ability, by rank in general ability, and in amount 
of reciting done. 

5. Percentages were found in the usual manner to the nearest 
tenth of a per cent. 

6.' Throughout the study participations by the class as a whole, 
i.e., in concert, are disregarded. 



14 Participation Among Pupils in Class- Room Recitations 



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V 

THE DISTRIBUTION OF PARTICIPATION BY 
GRADES* 

The pupils in all classes for which there were two or more 

records were ranked in order of the number of participations 

(see note) . By participation is meant any response on the part 

of the child whether in words or in action. When " Pupil 

recitation " is used, it is used as a synonym for participation. 

Table I shows the per cent of the total participating done by 

* The number of recitations or participations was the only measure of 
amount available for all schools. It may be asked whether this constitutes a 
true measure of amount, since a pupil really may say or do more in one long 
participation than in a number of shorter ones. It is interesting to note, how- 
ever, that from evidence which was secured from stenographic reports of lessons, 
the correlation between the amount of reciting as measured by the number of 
pupil's recitations and the amount of reciting done during each pupil recita- 
tion as measured by the number of words spoken, is a plus correlation; the 
correlations (Spearman foot-rule) being as follows: 





Number of Lessons 




Grade 


Reported 


Correlations 


1 


3 


.0 


2 


3 


.105 


3 


7 


.107 


4 


8 


.56 


5 


3 


.603 


6 


7 


.444 


7 


8 


.338 


8 


4 


.354 



The reports from which these correlations were secured, were not complete 
descriptions of the recitations of the various pupils, since in some cases the 
names of some of the pupils could not be secured by the stenographer, so 
that their participations could not be identified, but had to be marked 
" Pupil." The correlations given above were those made from the partici- 
pations of those pupils whose names were secured and so do not represent in 
any case the entire class. It seems safe to say, however, that it seems very 
unlikely that pupils reciting most frequently recite for shorter periods than do 
those reciting less frequently. On the contrary, it seems very probable and 
particularly so in the upper grades, that the pupils who recite most frequently 
also say or do most when they do recite. 

Since these stenographic reports were taken in Speyer School, which is an 
experimental school, and is not representative of public schools throughout 
the country, the author has made no attempt to use this information in gen- 
eralizing with regard to the same question in the case of the other teachers 
for whom data are given in this study. 

15 



16 Participation Among Pupils in Class- Room Recitations 

the first, second, third, and fourth quartiles of the pupils so 
ranked. 

The median is used throughout this study as the measure of 
the central tendency among the percentages of each quartile. 
The reasons for its use are those usually given; namely, its 
meaning is unambiguous and it is little affected by extreme 
measures. Below follow the medians for Table I. 







TABLE 


II 






Grade 




Quartiles 






1 


2 




3 


4 


1 


39.1 


27.4 




21.1 


11.7 


2 


40.5 


28.2 




20.0 


11.9 


3 


40.5 


28.2 




20.4 


10.4 


4 


43.5 


27.9 




20.1 


9.5 


5 


44.2 


27.6 




18.4 


7.6 


6 


37.3 


27.9 




22.0 


12.8 


7 


39.7 


27.2 




20.8 


12.2 


8 


40.7 


27.3 




20.0 


12.8 


9-12 


48.9 


27.3 




17.3 


8.3 



Median 40.5 27.6 20.1 11.7 

The question of reliability as it applies to the whole of the 
data has been treated in the preceding section and so need not 
be considered further here. A special question of reliability 
arises with regard to the data in this table, namely, that of in- 
ferring from two, three, or four records of a class, the true 
distribution of participation in this class, which would be shown 
by a greater number of records. It would have been very 
desirable to have ten or more records of each teacher whose 
practice is represented by the percentages in the table. Because 
of the great amount of time taken to secure these records, 
however, not all who cooperated could send this number. It 
became a problem, therefore, to determine the variability of 
percetnages representing a small number of records, from those 
taken from a number of records sufficient to give an adequate 
representation of the teacher's practice. This problem was found 
to be too complex to be solved in this study, and it involved 
influences which could not be separated in the data collected. 
For practical purposes, however, the influence of these small 
measures may be disregarded in determining the true median 
as can be seen by the fact that when they are thrown out, the 
medians or averages of the quartiles are little affected. The lack 



The Distribution of Participation by Grades 17 

of influence of these small measures in changing the median, 
might be inferred from the fact that they are well scattered 
throughout the distributions in Table I, there being as many 
percentages, taken from two or three records, below the median 
percentages as above; whereas if the percentages made from a 
small number of records had an influence in lowering or raising 
the medians of this table, they should be found chiefly above or 
below the medians, as the case might be. The medians of the 
medians for each grade as made respectively from two or more, 
three or more, and four or more records, are given below: 

TABLE III 

Number of Quartiles 

Records 12 3 4 

2ormore 40.5 27.6 20.1 11.7 

3ormore 40.8 27.9 20.4 10.4 

4ormore 41.6 27.8 19.8 11.1 

The medians which are used in the discussion which follows 
are those found from the percentages computed from two or 
more records. The conclusions would be no different for practical 
purposes if either of the other two sets of medians had been used. 

The measure of variability used is Q, the semi-inter-quartile 
range. The Q's for each quartile of each grade are given below: 







TABLE 


IV 






ADE 




Quartiles 






1 


2 




3 


4 


1 


6.0 


.7 




2.5 


4.5 


2 


3.3 


1.9 




2.2 


3.0 


3 


3.6 


1.1 




1.5 


3.3 


4 


5.4 


1.9 




1.4 


3.3 


5 


6.1 


.9 




2.0 


4.0 


6 


5.4 


1.4 




2.2 


5.8 


7 


3.5 


1.3 




1.3 


1.7 


8 


7.1 


1.3 




2.9 ■ 


2.6 



9-12 7.2 2.8 3.1 3.2 

College 3.0 2.7 2.6 2.0 

As shown by this table, the variability is greatest in the quartiles 
doing most and least reciting, and least in the two middle 
quartiles. 

Judging from the evidence in Table I, and using the above 
medians of the medians of percentages made from two or more 
records, for purposes of generalization, one would say that the 
fourth of the class doing most reciting does about one and three- 



18 Participation Among Pupils in Class- Room Recitations 

fifths of a pro rata share, (a pro-rata share being twenty-five 
per cent of all the reciting,) the second fourth about one and one- 
ninth of a pro-rata share, the third fourth about four-fifths of a 
pro-rata share, and the low fourth less than half of a pro-rata 
share; the percentages of a pro-rata share being respectively, 
162.0, 110.4, 80.4 and 46.8. The first quartile does about four 
times as much reciting as does the fourth. The significance of 
the inequality of this distribution will be taken up later in this 
study. 



VI 

THE RELATIONSHIP BETWEEN GENERAL ALL- 
ROUND ABILITY AND AMOUNT OF PARTICIPATION 

The preceding section considered the mere fact of inequality 
of distribution without taking into account any relationship 
between this inequality and any other fact. The problem of 
this section is to determine what the relationship is between 
general all-round ability and the amount of participation. 
General all-round ability is used in the sense defined in Part 2. 
The facts of this relationship are given in Table V. 

The relationship between general all-round ability and the 
amount of participating, is shown by comparing the first, second, 
third, and fourth quartiles in ability with the amount of reciting 
done by each. The reasons for using the quartile and the 
methods of determining it, were those given in Part IV, Section 
4. By the first quartile, is meant the best fourth of the class 
in general all-round ability; by the second quartile, the second 
fourth of the class in general all-round ability, etc., the pupils 
being ranked as described under II (B) of the directions on Sheet 
4. The amount of reciting done by each quartile is expressed as 
a percentage of the amount of reciting done by the whole class. 
For each class in this table, there are given the percentages corres- 
ponding to each quartile, the number of records from which these 
percentages were determined, the number of the pupils in the 
class, and the key number of the teacher of the class. By a class, 
is meant the administrative unit ordinarily referred to as a 
class, as for example, Class A, Grade VI. Where two or more 
measurements appear for the same teacher, this is descriptive of 
the fact that this teacher had charge of that number of separate 
classes. 

The median is used to show the central tendency of the quartile 
percentages of all the teachers in each grade. 

Three possible methods of finding these central tendencies 
suggest themselves : 

19 



20 Participation Among Pupils in Class- Room Recitations 

1. Take each percentage as the most reliable measure of the 
quartile of the class it represents without regard to the number 
of records from which this percentage was made. This has the 
disadvantage of giving the same weight to a percentage made from 
a single record (and which may, therefore, be an exceptional 
record,) as to percentages made from a large number of records, 
(and which, therefore, more probably represent the actual practice 
of the teacher). It will be noticed by a study of Table III, that 
most extremely low or extremely high measures are those which 
are made from one record of a class. 

2. Weight each measure by counting it a number of times 
equal to the number of records from which it is made. This 
offsets the difficulty mentioned under 1, but has the disadvantage 
of giving too much influence to School IV, for which the author 
personally made records, and for which a great number of records 
were made. Consequently, the position of the percentage 
representing this school would be very influential in determining 
the median for that grade. 

3. As a compromise, weight each measure by using the 
square root of the number of records from which the percentage 
was made. Proceed then as in 2. This method has a tendency 
to offset the difficulties mentioned above under 1 and 2, and 
probably approaches most nearly the true measure of the actual 
practice in the field. 

When the medians for each grade were found according to the 
methods described under 1 and 3, very little difference was found 
between the medians so obtained. In the first quartile, four 
differences are zero, three differences are less than one, and two 
differences are less than two. In the second quartile, three 
differences are zero, five differences are less than one, and one 
difference is less than two. In the third quartile, four differences 
are zero, three differences are less than one, and two differences 
are two or less. In the fourth quartile, two differences are zero, 
four differences are less than one, two differences are less than 
two, and one difference is less than four. In only one case, 
that of the fourth grade, does the difference amount to more than 
two (the median for the fourth quartile in this grade being 20.9, 
as found by method 1, and 17.2 as found by method 3). For 
practical purposes, therefore, and because of the greater sim- 
plicity, the medians found as described under 1 are the medians 



Relationship Between General Ability and Participation 21 



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22 Participation Among Pupils in Class- Room Recitations 



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Relationship Between General Ability and Participation 23 

which appear in Table VI, and which are used in the discussion 
which follows. 

TABLE VI 
Percentage of Reciting Done by Each Grade, Median Measures 
Grade Quartiles 





1 


2 


3 


4 


1 


28.2 


26.6 


22.3 


22.3 


2 


29.6 


23.8 


23.4 


23.9 


3 


27.3 


30.2 


22.6 


19.9 


4 


28.9 


24.1 


25.3 


19.1 


5 


28.0 


24.6 


23.3 


22.2 


6 


31.5 


24.2 


23.6 


21.8 


7 


28.1 


26.9 


23.3 


18.6 


8 


30.6 


24.7 


23.1 


19.7 


-12 


31.3 


26.1 


22.2 


16.5 


tAGES 


: 29.3 


25.7 


23.2 


20.4 


3: 


1.25 


1.25 


.4 


1.55 



Note: — Three records for the kindergarten give the following percentages: first quartile, 
32.1; second quartile, 26.0; third quartile, 20.2; fourth quartile, 21.7. 

Several facts of importance should be pointed out with regard 
to the preceding table. In using the average of the medians, 
as a most convenient single figure to describe the quartiles in 
the table, it may be pointed out that the first quartile does, 
roughly, about one and two-fifths times as much participating 
as does the lower quartile. The second quartile does slightly 
more than an equal share, the third quartile slightly less than an 
equal share of participation, the actual averages being 29.3, 
25.7, 23.2, 20.4. 

In no case does the median measure of the amount of reciting 
done by the best quartile fall below an equal share, and in no 
case does the sum of the percentages representing the reciting 
of the first and second quartiles fall as low as the sum of the per- 
centages representing the reciting done by the third and fourth 
quartiles combined. 

There is also a tendency for the per cent of reciting done by 
the best quartile to increase with an advancing grade, so that 
pupils in the upper grammar grades do more than those in the 
primary or intermediate schools, etc. The amount of reciting 
done by the second and third quartiles remains fairly constant 
throughout the grades, with this exception: that where the first 
quartile is relatively low in the percentage of reciting done, the 
second quartile is likely to be high, and vice versa. 





TABLE VII 




First 


QUARTILE 


Fourth Quartile 


r 5 Per. 


25 Per. 


75 Per. 25 Per 


32.4 


26.2 


25.0 18.7 


31.9 


25.9 


27.4 17.3 


31.8 


23.9 


23.1 16.8 


35.7 


26.9 


24.6 16.1 


32.8 


27.0 


27.6 18.9 


35.5 


25.9 


24.5 18.2 


38.3 


26.6 


20.8 15.1 


36.7 


25.0 


23.1 13.1 


42.8 


27.6 


19.1 11.1 



24 Participation Among Pupils in Class- Room Recitations 

As might be expected from the tendency in the first quartile, 
the amount of reciting done by the fourth quartile grows increas- 
ingly less with an advance in grade, so that in the high school, 
the best quartile does almost twice as much reciting as does the 
poorest quartile. This fact is shown still more clearly in the 
following table which gives for each grade, the seventy-five 
percentile and twenty-five percentile for the best and poorest 
quartiles of the class in ability. 

Grade 

1 
2 
3 

4 
5 
6 
7 
8 
9-12 

The 75 percentile in each case represents the point above 
which one-fourth of the cases rise; the 25 percentile, the point 
below which one-fourth of the cases fall. In the case of the 
quartile doing most reciting, the position of the point which marks 
the 75 percentile rose farther away from the median and is 
represented by a larger percentage, with an advance in grade. 
On the contrary, in the quartile doing least reciting, the 75 per- 
centile is represented by a percentage which grows increasingly 
less with an advance in grade. The 25 percentile is represented 
by a percentage which likewise decreases until in the high school 
one fourth of the cases fall below 1.1.1. 

The cases of teachers whose percentages rise above the 75 
percentile or below the 25 percentile, cannot be explained by 
the influence of single measures in allowing very unusual class 
recitations to be incorporated in the distribution, thus making 
it possible for unusually high and low percentages to increase the 
variability. The number of high and low percentages in each 
quartile which have been made from a large number of records, 
indicates that in the case of a considerable proportion of teachers, 
the amount of reciting done by the best quartile does exceed 
this 75 percentile division and the amount of reciting done by 
the poorest quartile does fall below the 25 percentile division. 



Relationship Between General Ability and Participation 25 

The measure of variability used is a modification of Q, the 
semi-inter-quartile range. From a glance at the measure given 
in Table V, it will be seen that the distribution is skewed. 
Accordingly, two measures of variability are used which the 
author has called Qi and Q 2) Qi being used to represent the range 
between the median and the 25 percentile; Q 2 being used to 
represent the range between the median and the 75 percentile. 
These measures of variability for each grade are given below: 









TABLE VIII 








ADE 








QUARTILE 












1 


2 




3 




4 






Qi 


Q 2 


Qi 


Q 2 


Qi 


Q 2 


Qi 


Q 2 


1 


2.0 


4.2 


1.6 


4.0 


3.3 


1.3 


3.6 


2.7 


2 


3.7 


2.3 


2.9 


4.5 


5.6 


3.7 


6.6 


3.5 


3 


3.4 


4.5 


1.1 


3.1 


4.5 


2.2 


3.1 


3.2 


4 


2.0 


6.8 


1.0 


5.0 


5.9 


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3.0 


5.5 


5 


1.0 


4.8 


3.3 


3.2 


5.8 


3.5 


3.3 


5.4 


6 


5.6 


4.0 


2.0 


1.4 


2.5 


1.4 


3.6 


2.7 


7 


1.5 


10.2 


2.6 


2.8 


3.9 


2.3 


3.5 


2.2 


8 


5.6 


6.1 


5.2 


6.8 


4.2 


3.2 


6.6 


3.4 


-12 


3.7 


11.5 


4.2 


4.9 


3.5 


5.7 


5.4 


2.6 



It will be noticed that in the first and second quartiles the 
variations below the median are much smaller than the varia- 
tions above it, the median of the variations being 3.4 for Qi, and 
4.8 for Q 2 in the first quartile, 2.6 for Qi and 4.0 for Q 2 in the 
second quartile. In the third and fourth quartiles, on the other 
hand, the variations below the median are larger than the varia- 
tions above it; the median of the Q x 's being 4.2 in the third and 
and 3.6 in the fourth quartile, and of the Q 2 's, 2.3 in the third and 
3.2 in the fourth quartile. The interpretation of the difference 
between the two Q's is probably this: it is very unlikely that the 
-pupils of ability can be kept much below an equal amount of par- 
ticipation; on the other hand, in cases where the conduct of the 
class is determined largely by the interest and initiative of the 
pupils, the amount of reciting done by this quartile may run very 
high. In the case of the third and fourth quartile, it seems un- 
likely that even the best drillmaster can get much more than an 
equal share of participation on the part of the duller pupils, 
while, on the other hand, in the case of teachers who leave the 
conduct of the class largely to the initiative of the pupils, these 
poorer pupils may do a very small proportionate part of the work 
of the class. 



26 Participation Among Pupils in Class- Room Recitations 

Variability among the various teachers within any grade is 
low when the small number of records for each teacher is taken 
into consideration. The sum of Qi and Q 2 is the range between 
the 25 percentile and the 75 percentile and therefore contains 
half the cases. As would be expected from the fact that the 
variability above the median is greater than that below it, in 
the case of the first two quartiles, and less in the case of the two 
lowest quartiles, half the cases can be gotten within a much 
smaller range by selecting the range toward the end of the lesser 
variations. For example, in the case of the first quartile, in 
Grade VII, the inter-quartile range lies between 26.6 and 38.3, 
and is equal to 11.7. Half the cases are contained, however, 
between 25.6 and 28.1, with a range of 2.5. 

Variability expressed by the Qi's and Q 2 's is somewhat larger 
than the true variability among teachers (which would be shown 
by a larger number of records for each teacher), owing to the 
fact that single records make possible the inclusion of very 
unusual class procedures in which the amount of the reciting 
done by each quartile may run very high or very low. Even 
allowing for the tendency for the percentage of reciting done 
by the first quartile to run higher as the grades advance and for 
the per cent of reciting done by the fourth quartile to become 
less with an advance in grade, the amount of variation among the 
medians of the various grades is remarkably small, as is shown 
by the Q's of the quartiles. The gross range of distribution 
for the medians which represent the tendencies for each grade, 
is from 27.3 to 31.5 in the first quartile; from 23.8 to 30.2 in 
the second; from 22.2 to 25.3, in the third; and from 16.5 to 
23.9 in the fourth. 

In the first quartile, two-thirds of the medians lie between 
28.0 and 30.6, with a range of 2.6; in the second quartile, two- 
thirds of the medians lie between 24.1 and 26.6, with a range of 
2.5; in the third, two-thirds of the medians lie between 22.6 
and 23.6, with a range of 1.0; in the fourth, two-thirds of the 
medians lie between 19.1 and 22.3 with a range of 3.2. 



VII 



RELATIONSHIP BETWEEN ABILITY IN SPECIAL 

SUBJECTS AND THE AMOUNT OF PARTICIPATION 

IN THOSE SUBJECTS 

The purpose of this portion of the study is to show the relation- 
ship existing between ability in special subjects and the amount 
of participating done in them. 

The data are given in Table IX, which is arranged after the 
manner described in Part VI, except that the rank in special 
ability is substituted for the rank in general allround ability. 
Otherwise, the arrangement of the data, the method of finding 
the central tendency, and the method of expressing variation 
is precisely that used in Part VI. 

For convenience in discussion, there is given in Table X the 
median measure for each subject. These medians are found 
from the individual percentages of the grades, ranking these 
measures in order of the amount of the percentage and without 
regard to grade. The median of each quartile represents, there- 
fore, the median of all the percentages in that quartile in all 
grades, for one subject. 

' Those subjects which would be described as formal subjects 
and which adapt themselves most easily to mechanical treatment 
are, as shown in Table X, lowest in amount of reciting done by 
the best quartile and highest in amount of reciting done by the 
lowest quartile. In one case — phonics — the amount of reciting 
done by the best quartile is less than an equal share. On the 
other hand, those subjects which would be ordinarily described 
as content subjects and which to an increasing degree demand 
problematic thinking and appreciation, are found to be relatively 
high in the amount of reciting done by the best quartile and low 
in amount of reciting done by the poorest quartile. In the case 
of phonics, spelling, and mathematics, the distribution among the 
quartiles is remarkably even, the first quartile doing about the 

27 



28 Participation Among Pupils in Class- Room Recitations 



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Relationship Between Special Subjects and Participation 29 





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30 Participation Among Pupils in Class- Room Recitations 



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Relationship Between Special Subjects and Participation 31 



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32 Participation Among Pupils in Class- Room Recitations 

same proportion of the total reciting as the fourth quartile in 
the case of phonics, and only slightly more in spelling and in 
mathematics. In geography, science, and literature, the first 
quartile does about one and one-half times as much reciting as 
does the fourth quartile. In English composition, history, 
social and industrial life, and in music, the distribution is very 
uneven, the first quartile doing from one and four-fifths to two 
and three-fourths as much reciting as does the fourth quartile. 
The percentages for School IV and School XVI (teachers 

TABLE X 
Medians for Special Subjects. All Grades Combined 

Subject Grade 1st Quar. 2nd Quar. 3rd Quar. 4th Quar. 

Phonics 1-5 24.6 22.1 27.0 24.5 

Spelling 1-8 27.4 24.1 23.7 23.9 

Mathematics. . . 1-12 27.6 24 . 9 22.8 23 . 8 

Languages 9-12 29.8 25.5 26.3 22.4 

Geography 3-8 29.1 25.5 21.4 19.7 

Reading and 

Literature... 1-12 30.5 25.0 22.7 19.7 
Composition and 

Grammar.... 1-8 31.5 23.8 22.8 17.4 

History 1-12 33.2 24.0 21.6 16.7 

Science 1-12 35.7 25.0 17.5 23.7 

Music 1-8 43.2 18.2 25.4 15.7 

38 to 56, and 191 to 194) should be noted here. These schools 
are attempting to make the course of study represent the most 
important activities of life outside the school and to provide 
in the fullest manner for the child's participation in and appre- 
ciation of these activities. Special stress is laid upon providing 
for initiative on the part of the pupil. The percentages for the 
teachers in these schools are almost uniformly above the median 
measures of the grade and subject in which they are found, for 
the first quartile, and below the medians for the fourth quartile. 
This is true also of the distributions in Tables I and V. The 
significance of this fact will be pointed out in Part VIII. 

The same general tendency for the percentages to grow larger 
for the first quartile and lower for the fourth quartile, with an 
advance in grade, which was pointed out in Parts V and VI, 
may be noticed in the case of special subjects, although the lack 
of a larger number of records prevents its being shown so clearly. 

The measure of variability used in this section is the same 



Relationship Between Special Subjects and Participation 33 

as that used in Part VI, Qi being used to represent the distance 
between the median and the 25 percentile; Q 2 , the distance 
between the median and the 75 percentile. These variations 
are given in Table XI, which follows. 



TABLE XI 

Subject 12 3 4 

Qi Q 2 Qi Q 2 Qi Q 2 Qi Q 2 

Mathematics 6.8 5.7 4.2 4.0 4.3 5.6 4.5 3.4 

Composition and Gram- 
mar 5.7 6.2 3.8 4.5 7.6 4.3 4.4 4.7 

Reading and Literature. 4.2 8.6 3.9 4.6 5.0 2.9 5.7 5.3 

History 3.1 11.0 4.0 4.3 5.3 4.2 5.1 6.4 

Geography 1.8 6.8 5.7 6.2 4.0 7.4 3.0 2.2 

Spelling 4.0 5.0 3.4 3.1 3.0 2.6 3.6 3.3 

Phonics 2.1 5.1 7.1 2.9 7.0 6.3 9.1 3.7 

Languages 7.4 4.1 .5 3.2 7.9 3.8 5.2 1.3 

Science 6.9 6.4 1.7 4.2 6.3 6.2 8.3 3.6 

Music 9.9 2.9 8.8 6.8 12.5 7.9 9.9 6.9 

Social and Industrial 

Life 9.6 7.1 9.0 4.6 3.4 4.3 8.1 3.8 



As in Parts V and VI, the variation above the median in 
quartiles 1 and 2 tends to be greater than the variation below it, 
while in quartiles 3 and 4 the reverse is true. In general, the 
variation is greatest in those subjects which are least adaptable 
for formal methods of teaching. Those subjects which are high- 
est in the amount of reciting done by the first quartile are in 
general highest in the amount of variation above the median; 
those which are lowest in the amount of reciting done by the 
fourth quartile are highest in the amount of variations below the 
median. The second and third quartiles show less variation 
than the first and fourth. 

The medians, variability, and quartile percentages have been 
given in the preceding portion of this part of the study for sub- 
jects for which the data are perhaps not extensive enough to 
warrant conclusive generalization. These data are all that were 
available for these subjects at the time of the publication of 
this study, and are given in order that those who may care to 
do so may supplement them by taking additional records. 
Those subjects in which records were marked for less than twenty 
teachers are given below, with a summary of the extent of the 
data for each : 



34 Participation Among Pupils in Class- Room Recitations 



Subject 

Languages 

Science 

Music 

Phonics 

Social and Industrial Life. 

The manner in which the tendencies shown by these data agree 
with those shown in the case of subjects for which the data are 
more extensive renders it unlikely that the central tendencies 
which would be computed from a greater number of records 
would vary greatly from those given. 



Number 


OF 


Number of 


Number of 


Teachers 


Classes 


Records 


5 




7 


9 


6 




9 


12 


8 




10 


14 


12 




14 


14 


13 




12 


37 



VIII 

EDUCATIONAL IMPLICATIONS 

It is the purpose of this part of the study to summarize the 
facts given in the preceding section, to give a further interpre- 
tation of these facts, and to trace some of the more important 
educational implications. 

The Gross Inequality: The opportunity for participation in 
the activities of the school is not equably distributed, the fourth 
of the class doing most reciting participating about four times 
as much as does the fourth of the class doing least reciting. The 
percentages of a pro-rata share of reciting are 162.0, 110.4, 80.4, 
46.8. The influence of differences in ability is not sufficient to 
wholly explain this inequality, which is uniformly greater than 
that found in the distributions according to ability. Other 
factors contribute to bring about this increase, of which the most 
important are differences among the pupils in initiative, aggres- 
siveness, talkativeness and attractiveness of personality. Data 
organized with the rank in these qualities substituted for that 
in ability show that in the case of each of these qualities the 
amount of the reciting done by the fourth of the class ranking 
highest in the quality, is greater than that done by the fourth 
of the class ranking lowest in the quality. This inequality is 
far less, however, than has been commonly supposed. 

Relationship Between General All-round Ability and Amount 
of Participation : The pupils who are ranked highest by the teacher 
in general all-round ability, participate more in the activities 
of the school than do those who are ranked lower; the best fourth 
doing about one and two-fifths as much reciting as the poorest 
fourth, the second fourth doing slightly more than an equal 
share, and the third fourth slightly less than an equal share. 
The inequality shown by these data is far lower than com- 
monly supposed. What inequality exists is probably due 

35 



36 Participation Among Pupils in Class- Room Recitations 

to the following factors: 1. Pupils who are most compe- 
tent, in general, desire most to participate. 2. Those who 
wish most to participate tend to get to do it. 3. The teacher 
feels the necessity of getting things done and so accepts the more 
ready and satisfactory answers of the bright pupils. 4. Human 
nature avoids error if possible, i.e., it is more pleasant to receive 
adequate contributions from pupils than those which are 
inadequate or incorrect. 

It is significant that in schools IV and XVI the percentages 
representing the amount of reciting done by the first quartile 
should be uniformly above the median for all schools. It seems 
clear from this that the adoption of the modern conceptions in 
education carries with it the necessity of facing anew the 
detailed problems of method and of class management. It is 
certain, for example, that the teacher who has for her ideal the 
development of initiative on the part of the pupils will have 
greater difficulty in controlling the distribution of opportunity 
for participation among her pupils. 

While it is true that the median percentage for each grade 
much more nearly approaches the pro-rata share for each 
quartile than has commonly been supposed, it should be pointed 
out that the large number of teachers shown by the data to have 
an inequality of distribution above the 75 percentile must 
constitute a special problem. It is these unusual cases which 
must receive the attention of the supervisor. 

Inequality of Distribution by Subjects. It is especially signi- 
ficant that the greatest equality of distribution should lie with 
those subjects which are most adaptable for formal treatment 
and pure memory work. For the most part, these subjects 
have been long in the curriculum, so that teachers through a 
period of many hundred years, have perfected and handed down 
mechanical procedures and devices for securing an equable 
distribution. In such cases, systems (such as card rolls, calling 
on the pupils by seats, in rows, or alphabetically) can be readily 
used. Subjects in which appreciation has to be developed or 
in which problems have to be sensed and solved, are not adaptable 
for such treatment. Appreciation and thinking cannot be ordered 
alphabetically, nor by rows, nor by card indexes. It is not strange, 
therefore, that subjects which have a problematic organization 
or which demand appreciation are shown by Table X to have the 



Educational Implications 37 

greatest inequality of distribution. With the modern tendency 
to increase the amount of problematic organization in the 
curriculum ; to demand that the course of study be tied up with 
life outside the school ; to insist that the pupil make out his own 
problems, and that he develop aesthetic and ethical appreciation ; 
the problem becomes increasingly important. That we have 
not reached a satisfactory solution is evidenced by the fact that 
the two schools which are perhaps among the foremost of the 
country in setting up these new standards (schools IV and XVI) 
are among those in which the inequality of distribution of oppor- 
tunity for participation is greatest. 

The Increase in Inequality With an Advance in Grade: The 
tendency for the inequality in distribution to grow greater with 
an advance in grade, seems to be an effect of the following 
causes: (1) With an advance in grade the subject matter grows 
more difficult and more interesting to the teacher, so that there 
is an increasing tendency for it to occupy the attention of the 
teacher to the exclusion of the problems of class procedure. 
(2) With an advance in grade, the greater age of the pupil 
makes him more able to make his personality felt, so that he 
may control class procedure to an increasing degree. (3) He 
is more and more concerned with the content, and less with 
getting the mere tools of knowledge. This seems to be the in- 
fluence, for example, which makes the percentage done by the 
best quartile in reading less, proportionately, in the lower grades 
than in the more advanced grades where the tools of reading 
are better in hand and the attention is more directed to the 
content of what he reads. 

To project solutions for these difficulties is not within the 
scope and province of this study. Its purpose has been fulfilled 
if it has described the practice with regard to the distribution 
of opportunity for participation, and has pointed out for this 
problem, the implications and significance of the modern de- 
mands for functional and problematic teaching. 



APPENDIX 

In the effort to estimate the reliability of percentages com- 
puted from a small number of records, the amount of reciting 
done by each quartile was computed from the first two records, 
according to date, of classes for which there were six or more 
records. The percentages representing the first and fourth 
quartiles, were then compared with the corresponding quartile 
percentages which had been found from the whole number of 
records. The two sets of percentages are given below: 





Highest 


Quartile 


Lowest 


Quartile 


Teacher 




6 or More 




6 or More 


Grade 1-8 


2 Records 


Records 


2 Records 


Records 


38 


40.1 


39.5 


8.6 


11.8 


124 


30.4 


34.0 


19.6 


15.2 


124 


31.6 


31.5 


19.7 


17.1 


128 


55.5 


44.1 


6.9 


7.8 


2 


37.8 


40.2 


15.5 


11.9 


39 


57.9 


40.8 


3.4 


6.7 


2 


52.7 


44.8 


4.1 


10.6 


125 


32.9 


41.2 


14.9 


10.4 


2 


51.8 


44.9 


4.0 


8.2 


58 


60.0 


40.2 


0.0 


10.4 


40 


62.4 


40.4 


0.0 


10.3 


126 


54.5 


43.5 


0.0 


12.7 


41 


44.0 


44.6 


8.6 


7.9 


42 


42.8 


41.6 


15.1 


12.0 


5 


43.1 


38.8 


4.8 


13.8 


43 


37.8 


34.5 


17.2 


18.0 


7 


49.7 


36.6 


11.2 


14.9 


44 


56.5 


47.2 . 


4.9 


10.0 


62 


62.4 


39.3 


6.0 


13.1 


45 


67.3 


50.4 


4.5 


9.0 


7 


62.4 


46.8 


9.2 


8.9 


7 


42.2 


40.7 


11.5 


9.2 



The quartile percentages found from all the records were 
subtracted from those found from two records only. The dif- 
ferences resulting were arranged in order, placing the largest 
minus difference at the low end' and the largest plus difference 
at the high end. The median of the differences so arranged is 
plus 7.4 for the first quartile and minus 3.3 for the fourth quar- 
tile. In the case of these 22 classes, therefore, the effect of 

38 



Appendix 39 

finding the percentages from two records only is to raise the 
percentages in the first quartile 7.4 and to lower the percentage 
in the fourth quartile 3.3. This is strangely inconsistent with 
the results shown in Part V, since it should be expected that 
casting out small records should have lowered the median for 
the first quartile and raised the median for the fourth, whereas 
the opposite was true. The only explanation for this inconsis- 
tency is the great number of factors which may enter to render 
percentages representing a small number of records unreliable. 
The chief of these are as follows: 

1. The pupils represented by a small number of records as 
doing most reciting may not be the pupils who really would be 
shown to do most reciting by a greater number of records. 

2. If the teacher is subject to an influence which makes for 
an inequality of distribution, it cannot be certain from a small 
number of records : 

a. That this influence operated, 

b. That it did not operate more than usual. 

3. Because of limitations due to fixed class periods, it seems 
probable that certain pupils may be neglected for one or two 
recitations. This would, of course, lower the percentage repre- 
senting the amount of reciting done by the low quartile, and raise 
the percentage representing the amount of reciting done by the 
high quartile. It is obvious, however, that these pupils are not 
neglected indefinitely so that if more records were taken, the 
percentage for the low quartile would tend to be raised, and the 
percentage for the high quartile, lowered. 

4. It may be possible that the two records represent very 
formal procedure on the part of the teacher, such as would be 
found in a drill lesson in Arithmetic, where pupils are called 
upon in turn. 

Very obviously, some of these influences would tend to lower 
the percentages representing the amount of reciting done by 
the first quartile and to raise the percentages representing the 
amount of reciting done by the fourth quartile; while others 
would have the opposite effect. It is impossible to tell, however, 
from the data at hand, which of these influences has operated 
in the case of any given percentage. 

It seems very improbable that these influences should have 



40 Participation Among Pupils in Class- Room Recitations 

operated by chance in the case of the 22 classes given above 
in such a manner as to effect the change noted, while at the same 
time, and by the same chance combination, they should have 
combined so as to have no effect in fixing the medians in Table 1 . 
Under the circumstances, it seems that the evidence is against 
the true medians being higher for the first quartile and lower 
for the fourth quartile than those given in Table 2, while there 
is some reason for believing that the true medians may be some- 
what lower for the first quartile and higher for the fourth 
quartile, than those given in this table. 



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